The principle of using a pair of matched MRs in a differential arrangement for the purpose of measuring small linear displacements along one dimension is well known in the art. FIG. 1 depicts one such example. In FIG. 1, MR die 10 is composed of two matched MRs, MR1 and MR2, a first terminal 16, a second terminal 18, and a third terminal 20. A small moving target 22, in the form of a permanent magnet if the die is not biased by an external magnetic field, or, if the MR die 10 is biased by an external magnetic field, then the target would, instead, be a ferromagnetic material. The target 22 is suspended, usually a fraction of a millimeter, above the MR die 10. A two dimensional Cartesian (X-Y) coordinate system 30 consisting of an X axis and a Y axis is superimposed on the MR die 10 as shown in FIG. 1, whereby the target 22 is movable along the X axis.
It is well known in the art that the resistance, R.sub.MR, of an MR can be modulated by a varying magnetic flux density through the MR, which, in turn, varies the resistance of the MR. The portions of MR1 and MR2 under the target 22 are exposed to a considerably higher magnetic field than the portions of MR1 and MR2 not under the target. Thus, the more area of MR1 or MR2 covered by the target 22, the greater the resistance of MR1 or MR2, respectively. When the center line 24 of the target 22 coincides with the Y axis, which is aligned midway between MR1 and MR2, the areas of MR1 and MR2 covered by the target are equal and, thus, the resistance R.sub.MR1 of MR1 is the same as the resistance R.sub.MR2 of MR2, since MR1 is matched with MR2. Once the target 22 is moved in, for example, the positive X direction to the point where the center line 24 of the target is at the position 36 on the X axis, the area of MR1 covered by the target is less than the area of MR2 covered by the target, thereby causing the resistance of MR2 to increase while the resistance of MR1 decreases. A properly designed electrical circuit, as will be discussed shortly, can incorporate this change in resistance and produce an output voltage which is a linear function of the position of the target 22 relative to MR1 and MR2.
Such a circuit is depicted in FIG. 2. The first terminal 16 of MR1 is connected to the positive terminal 38 of a constant voltage source V.sub.IN whereas the third terminal 20 of MR2 is connected to ground 40. Resistors R1 and R2 have, preferably but not necessarily, the same value. V.sub.OUT is measured with respect to a pair of output terminals 42, 44.
With resistors R1 and R2 having the same value, V.sub.OUT can be expressed in terms of the current I.sub.MR passing through MR1 and MR2 and the resistances, R.sub.MR1 and R.sub.MR2, of MR1 and MR2, respectively, as: EQU V.sub.OUT =(I.sub.MR /2)(R.sub.MR2 -R.sub.MR1) where I.sub.MR =V.sub.IN (R.sub.MR2 +R.sub.MR1).
The movement of the target 22 of FIG. 1 in the X direction increases the resistance of one MR and decreases the resistance of the other MR. However, since the MRs are matched, the magnitude of the increase of the resistance of one MR is the same as the magnitude of the decrease in resistance of the other MR, thereby causing the total resistance (R.sub.MR2 +R.sub.MR1) to remain constant whereby the current MR also remains constant.
Thus, the output voltage, V.sub.OUT, is directly proportional to the difference in the respective resistance of MR2 and MR1 and, hence, is a linear function of (R.sub.MR2 -R.sub.MR1). Since the resistance of each MR is proportional to the area covered by the target 22 and the area covered is proportional to the position of the target along the X axis (wherein, the position of the target along the Y axis remains constant), the output voltage, V.sub.OUT, is directly proportional to the position of the target along the X axis, as well.
However, there are many applications requiring two dimensional position sensors. Probably, the most famous application of this kind is the ubiquitous computer mouse employing a rubber covered ball, two rollers, and two position encoders. A two dimensional position sensor utilizing MR elements could be envisioned as an MR die consisting of an overlay of two orthogonal MR layers, with each layer composed of two MR elements. Unfortunately, two layer MRs are not practical and the die pattern would be, in effect, reduced to one layer consisting of four independent MR elements which would require the use of active components, such as operational amplifiers, to realize a two dimension position sensor.
Accordingly, what remains needed in the art is a solution to the problem of providing an MR die for a two dimensional position sensor which does not, necessarily, require the use of active components.